1. The Illinois Department of Transportation is considering building a new highway on a route described below. This highway will be fully equipped with tolling technology.
a. If the highway is built with two lanes. What will be the efficient short-run traffic volume? Explain.
b. For the efficient volume what is the efficient toll?
c. What is the value of the average fixed cost at the efficient volume? Explain.
d. What is the efficient volume, toll and average fixed cost if the highway is built with four lanes? Explain.
e. Is it efficient to build the highway with four lanes? Explain.
2. Consider the following data table for a commuter making modal choice between auto, bus and fixed rail in the town of Bigville. Notice the calculations here suggest that auto will be the chosen mode.
a. How much of a reduction in line-haul time would be necessary to make fixed rail the chosen mode?
b. Is there a fare reduction that can make bus the chosen mode? If so how much would it be?
c. How much of an increase in parking fees would be necessary to make auto no longer the chosen mode? Which mode would now be chosen?
d. What happens to the modal choice if the rider has a wage of only $6 per hour?
3. The basic expression for the user cost of owner occupied housing is ((1-τ)(i+h)+d-g)v, where τ is the household's income tax rate, i is the mortgage interest rate, h is the property tax rate, d is the depreciation rate, g is the rate of capital gains and v is the purchase price per unit of housing. The user cost of rental housing is given by (i+h+d-g)v - λev/(1-λ), where λ is the landlord's income tax rate, and e is the rate of excess depreciation allowed to landlords.
a. Draw a graph showing user cost of owner occupied housing as a function of households' tax rates (τ). Explain the shape of this graph.
b. Add a line representing user cost of rental housing to the graph from part (a). Explain the shape of the new line.
c. On the graph identify τ*, the cut-off tax rate that divides renters and owners. Explain the logic of the resulting model of tenure choice.
d. Indicate on your graph what will happen if i, the interest rate falls and g, rate of capital gains rises. Be sure to indicate how this change affects τ*.
e. Explain the relevance of your observation in part (d) to the country's experience in last decade's housing bubble.
4. The Detroit housing sector consists of three submarkets, high quality, medium quality and low quality. Assume at first that all three submarkets have perfectly inelastic supply curves.
a. Draw supply and demand diagrams for each submarket.
b. The demand curve in the middle submarket now shifts down as the result of the outmigration of middle class households. Keeping supply curves perfectly inelastic, draw new supply and demand diagrams showing the new equilibrium positions in each submarket. Explain the changes in equilibrium illustrated in these new figures.
c. Explain why the assumption of perfect inelasticity in the low-quality market may be unreasonable. Make clear what assumption might be more reasonable. Redraw the initial supply-demand curves for the low quality market under the new assumption.
d. Using the figure from part c, show the effects in the low quality market of the initial downward shift in demand in the middle submarket. Explain what is happening.
e. Does your analysis in part d suggest that the outmigration of middle income households generates any externalities in neighborhoods with low-quality housing? Explain.